2017/01/09 by Chebolu, Sunil K., Lockridge, Keir
#16U60 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1701.02341
Laszlo Fuchs posed the following problem in 1960, which remains open: classify the abelian groups occurring as the group of all units in a commutative ring. In this note, we provide an elementary solution to a simpler, related problem: find all cardinal numbers occurring as the cardinality of the group of all units in a commutative ring. As a by-product, we obtain a solution to Fuchs' problem for the class of finite abelian p-groups when p is an odd prime.